2.062J | Spring 2017 | Graduate
Wave Propagation

Lecture Notes


Chapter 1: Sample Wave Problems (PDF)

  • Transverse Vibration of a Taut String
  • Longitudinal Vibration of an Elastic Rod
  • Traffic Flow on a Freeway
  • Wave Propagation in Arteries
  • Shallow Water Waves and Linearization
  • Sound in Fluids
  • Flexural Waves in a Beam on an Elastic Foundation


Chapter 2: One Dimensional Waves (PDF)

  • General Solution to Wave Equation
  • Branching of Arteries
  • Waves in an Infinite Domain due to Initial Disturbances
  • Reflection from the Fixed End of a String
  • Forced Waves in an Infinite Domain
  • String Embedded in an Elastic Surrounding
  • Dispersion from a Localized Initial Disturbance
  • Scattering of Sinusoidal Waves
  • General Identities in Scattering by Arbitrary in Homogeneities
  • Refraction in a Slowly Varying Medium


Chapter 3: Two Dimensional Waves (PDF - 2.4MB)

  • Reflection and Transmission of Sound at an Interface
  • Equations for Elastic Waves
  • Free Waves in Infinite Space
  • Elastic Waves in a Plane
  • Reflection of Elastic Waves from a Plane Boundary
  • Scattering of Monochromatic SH Waves
  • Diffraction of SH Wave by a Long Crack
  • Rayleigh Surface Waves
  • Elastic Waves due to a Load Traveling on the Ground Surface
  • Partial Wave Expansion
  • Approximate Evaluation of an Integral


Chapter 4: Waves in Water (PDF)

  • Governing Equations for Waves on the Sea Surface
  • Progressive Waves on a Sea of Constant Depth
  • Wave Resistance of a Two-dimensional Obstacle
  • Narrow-banded Dispersive Waves in General
  • Radiation of Surface Waves Forced by an Oscillating Pressure
  • The Kelvin Pattern of Ship Wave
  • Basic Theory for Two-dimensional Internal Waves in a Stratified Fluid
  • Internal Waves Modes for Finite N
  • Internal Waves in a Vertically Unbounded Fluid
  • Reflection of Internal Waves at Boundary


Chapter 5: Wave Localization (PDF)

  • Wave Localization in a Random Medium
  • References


Chapter 6: Forced Dispersive Waves Along a Narrow Channel (PDF)

  • Free Wave Propagation Along a Narrow Waveguide
  • Forced Wave Propagation Along a Narrow Waveguide
  • Initial Boundary Value Problem


Chapter 7: Internal Waves in a Stratified Fluid (PDF - 1.1MB)

  • Introduction
  • Governing Equations for Incompressible Density-stratified Fluid
  • The Buoyancy Frequency (Brunt-Vaisala Frequency)
  • Internal Gravity Waves in Unbounded Stratified Fluid
  • Waveguide Behavior